How Big is the Moon?

This relates to last week's snack, "How big is the sky?" We found that the sky is about 40,000 square degrees. Now we also know that there are about 6000 stars visible to the naked eye. So there must be 6000/40,000=0.15 stars per square degree. So how big is the Moon?

The Moon has a radius on the sky of about 1/4 a degree. The area of a circle is pi * radius^2, so the Moon's area is pi * (1/4)^2=0.2 square degrees.

So the number of stars in an area the size of the Moon is 0.15 stars/square degree * 0.2 square degrees=0.03 stars per Moon area. That means that the Moon, on average, covers 0.03 stars. In other words, you would have to move the Moon around 30 times before covering a single star!

Your eye is tricking you when you go outside at night. The sky seems full of stars, and the Moon looks big! But really, it's the sky that's big, and the Moon is small.

One trick here, though: the stars are not randomly strewn throughout the sky, but tend to cluster more in some areas than others. The density of stars is much higher in the constellation of Sagittarius, for example, because that direction is toward the center of the Milky Way. If the Moon were there, it would almost certainly cover up several stars!